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Journal article
Behavior of a Model Dynamical System with Applications to Weak Turbulence
Experimental mathematics, v 22(3), pp 250-264
03 Jul 2013
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Abstract
We experimentally explore solutions to a model Hamiltonian dynamical system recently derived to study frequency cascades in the cubic defocusing nonlinear Schrodinger equation on the torus. Our results include a statistical analysis of the evolution of data with localized amplitudes and random phases, which supports the conjecture that energy cascades are a generic phenomenon. We also identify stationary solutions and periodic solutions in an associated problem, and find experimental evidence of hyperbolic behavior. Many of our results rely on reframing the dynamical system using a hydrodynamic formulation.
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Details
- Title
- Behavior of a Model Dynamical System with Applications to Weak Turbulence
- Creators
- James E. Colliander - University of TorontoJeremy L. Marzuola - University of North Carolina at Chapel HillTadahiro Oh - University of EdinburghGideon Simpson - University of Minnesota
- Publication Details
- Experimental mathematics, v 22(3), pp 250-264
- Publisher
- Taylor & Francis
- Number of pages
- 15
- Grant note
- Universitat Bielefeld DE-SC0002085 / DOE; United States Department of Energy (DOE) NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC) OISE-0967140 / NSF; National Science Foundation (NSF) University of North Carolina 250233-12 / NSERC through RGPIN
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000327834700003
- Scopus ID
- 2-s2.0-84887873199
- Other Identifier
- 991019296576504721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics